Exploiting Combination Effect for Unsupervised Feature Selection by $\\ell_{2,0}$ Norm

Abstract

In learning applications, exploring the cluster structures of the high dimensional data is an important task. It requires projecting or visualizing the cluster structures into a low dimensional space. The challenges are: 1) how to perform the projection or visualization with less information loss and 2) how to preserve the interpretability of the original data. Recent methods address these challenges simultaneously by unsupervised feature selection. They learn the cluster indicators based on the $k$ nearest neighbor similarity graph, then select the features highly correlated with these indicators. Under this direction, many techniques, such as local discriminative analysis, nonnegative spectral analysis, nonnegative matrix factorization, etc., have been successfully introduced to make the selection more accurate. In this paper, we focus on enhancing the unsupervised feature selection in another perspective, namely, making the selection exploit the combination effect of the features. Given the expected feature amount, previous works operate on the whole features then select those of high coefficients one by one as the output. Our proposed method, instead, operates on a group of features initially then update the selection when a better group appears. Compared to the previous methods, the proposed method exploits the combination effect of the features by $\\ell {}_{2,0}$ norm. It improves the selection accuracy where the cluster structures are strongly related to a group of features. We conduct the experiments on six open access data sets from different domains. The experimental results show that our proposed method is more accurate than the recent methods which do not specially consider the combination effect of the features.